The Market is Up and the VIX is Down – How Much Extra Investing Info Do We Have?

I have written extensively on my blog about the relationship between the returns of assets and their volatility. It is a point of interest. Commentators on financial television frequently discuss the performance of the VIX and compare it to the performance of the market. This common usage leads us to believe that the VIX is a factor we should pay a lot of attention to.

 But empirically we do not see this. What we see is that the daily returns of the market, for which I'll take the returns of the SPY ETF, and the returns of the VIX, for which I'll take the returns of the VXX ETF are stabily and extremely negatively correlated. The chart below illustrates a linear regression of the returns of VXX onto the returns of SPY for several recent years of daily data. This negative relationship is extremely clear and strong (the R2 is some 69%, which is a big value for the returns of different assets in finance — it's equivalent to a correlation of −83%).

From a statistical point of view: when the market goes up the VIX goes down and when the market goes down the VIX goes up. Now these assets are not identical and their long-term trends do differ, hopefully the market ultimately drifts upwards whereas the VIX mean-reverts about a “typical” value, but on a daily basis they really disagree completely on direction in a very predictable manner.

In finance we are interested in assets that diversify our portfolio. This means that when add an asset to our portfolio the consequence ought to be that the net variance of the whole portfolio decreases. In their book on active portfolio management, Grinold & Kahn give the following formula for the risk of a portfolio of N assets all of which have a common pairwise correlation coefficient


This is actually one of my favourite sections in the whole book. It's simple, and brings home the rule that what we want to invest in are uncorrelated assets. The VIX is negatively correlated, but from a risk management point of view the sign of the correlation coefficient is less interesting than its closeness to zero. After all the sign just tells you to short the asset rather than go long it.